##### Department of Mathematics,

University of California San Diego

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### Math 209: Number Theory Seminar

## Bryan Hu

#### UC San Diego

## Critical values of the adjoint L-function of U(2,1) in the quaternionic case

##### Abstract:

We will discuss questions surrounding automorphic L-functions, particularly Deligne’s conjecture about critical values of motivic L-functions. In particular, we study the adjoint L-function of U(2,1).

Hundley showed that a certain integral, involving an Eisenstein series on the exceptional group G_2, computes this L-function at unramified places. We discuss the computation of this integral at the archimedean place for quaternionic modular forms, and how this relates to Deligne's

conjecture.

### May 16, 2024

### 2:00 PM

APM 6402 and online (see https://www.math.ucsd.edu/~nts

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